Once you have caught a number of Pokemon, you will realize just what supplies that you need to start increasing your Pokemon's Combat Points. You can access the ability to power up the Pokemon through the Pokemon tab. Underneath the Pokemon's portrait you will find the option to power up your Pokemon.
The more you raise your Pokemon's CP, the more it will cost to do so in the future. It maxes out at a particular point. How much you can raise your CP is dependent on your Trainer Level. The higher it is, the more you can raise a Pokemon's Combat Points.
When you have collected enough of the Pokemon's candy, you will be able to evolve the Pokemon. Just how much depends on the Pokemon itself. Some Pokemon, who evolve early, only need 12 candies. Others will evolve with 25 or 50 candies. Magikarp though, requires 400 candies to evolve. Each will be listed on the Pokemon's page.